van Donkelaar C C, Willems P J, Muijtjens A M, Drost M R
Department of Movement Sciences, Cardiovascular Research Institute Maastricht (Carim), The Netherlands.
J Biomech. 1999 Aug;32(8):755-62. doi: 10.1016/s0021-9290(99)00073-1.
An important assumption in 2D numerical models of skeletal muscle contraction involves deformation in the third dimension of the included muscle section. The present paper studies the often used plane strain description. Therefore, 3D muscle surface deformation is measured from marker displacements during isometric contractions at various muscle lengths. Longitudinal strains at superficial muscle fibers ( - 14 +/- 2.6% at L0, n = 57) and aponeurosis (0.8 +/- 0.9% at L0) decrease with increasing muscle length. The same holds for transverse muscle surface strains in superficial muscle fibers and aponeurosis, which are comparable at intermediate muscle length, but differ at long and short muscle length. Because transverse strains during isometric contraction change with initial muscle length, it is concluded that the effect of muscle length on muscle deformation cannot be studied in plane strain models. These results do not counteract the use of these models to study deformation in contractions with approximately - 9 % longitudinal muscle fiber strain, as transverse strain in superficial muscle fibers and in aponeurosis tissue is minimal in that case. Aponeurosis surface area change decreases with increasing initial muscle length, but muscle fiber surface area change is - 11%, independent of muscle length. Assuming incompressible muscle material, this means that strain perpendicular to the muscle surface equals 11%. Taking the relationship between transverse and longitudinal muscle fiber strain into account, it is hypothesized that superficial muscle fibers flatten during isometric contractions.
骨骼肌收缩二维数值模型中的一个重要假设涉及所包含肌肉截面在第三维度上的变形。本文研究了常用的平面应变描述。因此,在不同肌肉长度的等长收缩过程中,通过标记位移测量了三维肌肉表面变形。浅表肌纤维的纵向应变(在L0时为-14±2.6%,n = 57)和腱膜的纵向应变(在L0时为0.8±0.9%)随肌肉长度增加而降低。浅表肌纤维和腱膜的横向肌肉表面应变情况相同,在中等肌肉长度时相当,但在长肌肉长度和短肌肉长度时不同。由于等长收缩过程中的横向应变随初始肌肉长度而变化,因此得出结论,在平面应变模型中无法研究肌肉长度对肌肉变形的影响。这些结果并不妨碍使用这些模型来研究纵向肌肉纤维应变约为-9%的收缩中的变形,因为在这种情况下,浅表肌纤维和腱膜组织中的横向应变最小。腱膜表面积变化随初始肌肉长度增加而减小,但肌纤维表面积变化为-11%,与肌肉长度无关。假设肌肉材料不可压缩,这意味着垂直于肌肉表面的应变等于11%。考虑到横向和纵向肌纤维应变之间的关系,推测浅表肌纤维在等长收缩过程中会变平。